虚非完整约束的几何方法
Virtual Nonholonomic Constraints: A Geometric Approach
摘要：
虚拟约束是通过反馈施加在控制系统上的不变关系，与作用在系统上的真实物理约束相反。非完整系统是指速度具有不可积约束的力学系统。在这项工作中，我们介绍了虚拟非完整约束的几何框架中的概念。更确切地说，它是与仿射连接机械控制系统相关联的受控不变分布。我们证明了存在性和唯一性的控制律定义了一个虚拟的非完整约束，我们的特点是作为一个机械系统与诱导约束连接的解决方案的闭环系统的轨迹。此外，我们描述了非完整系统的动力学的虚拟非完整约束，即，我们刻画了何时可以从虚拟非完整约束获得非完整动力学。
英文摘要：
Virtual constraints are invariant relations imposed on a control system via feedback as opposed to real physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints on the velocities. In this work, we introduce the notion of virtual nonholonomic constraints in a geometric framework. More precisely, it is a controlled invariant distribution associated with an affine connection mechanical control system. We demonstrate the existence and uniqueness of a control law defining a virtual nonholonomic constraint and we characterize the trajectories of the closed-loop system as solutions of a mechanical system associated with an induced constrained connection. Moreover, we characterize the dynamics for nonholonomic systems in terms of virtual nonholonomic constraints, i.e., we characterize when can we obtain nonholonomic dynamics from virtual nonholonomic constraints.
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